Question

$overleftrightarrow{o q}$ and $overleftrightarrow{r t}$ are parallel lines.
which angles are alternate interior angles?
$\angle o p s$ and $\angle q p s$ $\angle o p s$ and $\angle o p n$
$\angle o p s$ and $\angle t s p$ $\angle o p s$ and $\angle t s u$

Explanation:

Alternate interior angles are formed when a transversal intersects two parallel lines. They lie between the two parallel lines and on opposite sides of the transversal.

• $\angle OPS$ and $\angle QPS$: These are adjacent angles, not alternate interior angles.
• $\angle OPS$ and $\angle OPN$: These are adjacent angles (linear - pair), not alternate interior angles.
• $\angle OPS$ and $\angle TSP$: Since $OQ\parallel RT$ and $NU$ is the transversal, $\angle OPS$ and $\angle TSP$ lie between the parallel lines $OQ$ and $RT$ and on opposite sides of the transversal $NU$.
• $\angle OPS$ and $\angle TSU$: These are not alternate interior angles as their position does not meet the criteria of alternate interior angles (formed by the intersection of a transversal with two parallel lines).

Answer:

$\angle OPS$ and $\angle TSP$